A viability theorem for set-valued states in a Hilbert space |
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Authors: | Thomas Lorenz |
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Affiliation: | Applied Mathematics, RheinMain University of Applied Sciences, 65197 Wiesbaden, Germany |
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Abstract: | Applications in robust control problems and shape evolution motivate the mathematical interest in control problems whose states are compact (possibly non-convex) sets rather than vectors. This leads to evolutions in a basic set which can be supplied with a metric (like the well-established Pompeiu–Hausdorff distance), but it does not have an obvious linear structure. This article extends differential inclusions with state constraints to compact-valued states in a separable Hilbert space H. The focus is on sufficient conditions such that a given constraint set (of compact subsets) is viable a.k.a. weakly invariant. Our main result extends the tangential criterion in the well-known viability theorem (usually for differential inclusions in a vector space) to the metric space of non-empty compact subsets of H. |
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Keywords: | Evolution inclusion Reachable set Viability condition Set differential inclusion Scalar topology Bounded scalar convergence |
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